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Chapter 12: Problem 458

When a security has a maturity value of \(\$ 100,000\) and the coupon rate is \(5 \%\), what are you willing to pay for it when it is due next year and the yield is \(9 \%\) ?

Short Answer

Expert verified
If the yield is \(9 \% \), you are willing to pay \(\$96,330.28\) for the bond today when it is due next year.

Step by step solution

01

Determine the Coupon Payment

First, we need to find the annual coupon payment, which is based on the maturity value and coupon rate. The coupon payment can be calculated as follows: Coupon Payment = Maturity value × Coupon rate Remember that the percentage should be converted to its decimal equivalent: Coupon rate = \(5\% = 0.05\)
02

Calculate the Coupon Payment

Now, we can calculate the Coupon Payment using the above formula. Coupon Payment = \(100,000 \times 0.05=\$5,000\) The annual coupon payment is \(\$5,000\).
03

Determine the Present Value of the Coupon Payment and Maturity Value

Now, we will find the present value of the bond using the yield as the discount rate. Present value (PV) is calculated as follows: PV = Cash Flows / (1 + Discount Rate)^n Where Cash Flows represent the coupon payment and maturity value, Discount Rate is the yield, and n is the number of years until maturity. In our case, n = 1. We will calculate the present value of both the coupon payment and the maturity value.
04

Calculate the Present Value of the Bond

1. Calculate the present value of the coupon payment: PV_Coupon = \(5,000 / (1 + 0.09)^1 =\$4,587.16\) 2. Calculate the present value of the maturity value: PV_Maturity = \(100,000 / (1 + 0.09)^1 =\$91,743.12\) 3. Add the present values of the coupon payment and maturity value to determine the total present value of the bond: Total Present Value = PV_Coupon + PV_Maturity =\(4,587.16+\$91,743.12=\$96,330.28\) Hence, if the yield is \(9 \%\), you are willing to pay \(\$96,330.28\) for the bond today when it is due next year.

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Most popular questions from this chapter

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